Green’s Dictionary of Slang

(Aus.) a temper tantrum.

1987		K. Lette Girls’ Night Out (1995) 106: But if you threw a tanty or two she’d do it, I reckon.
1997		J. Birmingham Tasmanian Babes Fiasco (1998) 78: They are approaching the red zone of an explosive Tunguska tanty.
2018		R. O’Neill ‘Ocker’ in The Drover’s Wives (2019) 180: Jacky chucked a bit of a tanty.